Question

A suspicious-looking man runs as fast as he can along a moving sidewalk from one end to the other, taking 2.60 s. Then security agents appear, and the man runs as fast as he can back along the sidewalk to his starting point, taking 14.0 s. What is the ratio of the man's running speed to the sidewalk's speed?

Answer 1

`(v_2)/(v_1) = 1.45`

Step-by-step explanation:

Let the side walk is moving as speed v1 and the fastest possible speed of the man is v2

so man will move from one end to other end in 2.60 s and let the length of the sidewalk is L

so we have

`L = (v_1 + v_2)2.60`

when the man runs back again to starting point then we have

`L = (v_2 - v_1)14`

now we have

`(v_2 - v_1)14 = (v_1 + v_2)2.60`

`5.38 v_2 - 5.38 v_1 = v_1 + v_2`

`4.38 v_2 = 6.38 v_1`

now we have

`(v_2)/(v_1) = (6.38)/(4.38)`

`(v_2)/(v_1) = 1.45`